100842: [AtCoder]ABC084 C - Special Trains

Problem Statement

A railroad running from west to east in Atcoder Kingdom is now complete.

There are $N$ stations on the railroad, numbered $1$ through $N$ from west to east.

Tomorrow, the opening ceremony of the railroad will take place.

On this railroad, for each integer $i$ such that $1≤i≤N-1$, there will be trains that run from Station $i$ to Station $i+1$ in $C_i$ seconds. No other trains will be operated.

The first train from Station $i$ to Station $i+1$ will depart Station $i$ $S_i$ seconds after the ceremony begins. Thereafter, there will be a train that departs Station $i$ every $F_i$ seconds.

Here, it is guaranteed that $F_i$ divides $S_i$.

That is, for each Time $t$ satisfying $S_i≤t$ and $t％F_i=0$, there will be a train that departs Station $i$ $t$ seconds after the ceremony begins and arrives at Station $i+1$ $t+C_i$ seconds after the ceremony begins, where $A％B$ denotes $A$ modulo $B$, and there will be no other trains.

For each $i$, find the earliest possible time we can reach Station $N$ if we are at Station $i$ when the ceremony begins, ignoring the time needed to change trains.

Constraints

• $1≤N≤500$
• $1≤C_i≤100$
• $1≤S_i≤10^5$
• $1≤F_i≤10$
• $S_i％F_i=0$
• All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$
$C_1$ $S_1$ $F_1$
$:$
$C_{N-1}$ $S_{N-1}$ $F_{N-1}$

Output

Print $N$ lines. Assuming that we are at Station $i$ $(1≤i≤N)$ when the ceremony begins, if the earliest possible time we can reach Station $N$ is $x$ seconds after the ceremony begins, the $i$-th line should contain $x$.

Sample Input 1

3
6 5 1
1 10 1

Sample Output 1

12
11
0

We will travel from Station $1$ as follows:

• $5$ seconds after the beginning: take the train to Station $2$.
• $11$ seconds: arrive at Station $2$.
• $11$ seconds: take the train to Station $3$.
• $12$ seconds: arrive at Station $3$.

We will travel from Station $2$ as follows:

• $10$ seconds: take the train to Station $3$.
• $11$ seconds: arrive at Station $3$.

Note that we should print $0$ for Station $3$.

Sample Input 2

4
12 24 6
52 16 4
99 2 2

Sample Output 2

187
167
101
0

Sample Input 3

4
12 13 1
44 17 17
66 4096 64

Sample Output 3

4162
4162
4162
0